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Research on Isolated Small Groups in Public Opinion Propagation Based on Cellular Automata Model

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2017 2nd International Conference on Computer, Mechatronics and Electronic Engineering (CMEE 2017) ISBN: 978-1-60595-532-2

Research on Isolated Small Groups in Public Opinion Propagation

Based on Cellular Automata Model

Bo-shu LI

1

, Shou-kui SI

2,*

and Xi-jing SUN

2

1

Graduate Students’ Brigade, Naval Aviation University, Yantai Shandong 264001, China

2

School of Basic Sciences for Aviation, Naval Aviation University, Yantai Shandong 264001, China

*Corresponding author

Keywords:Public opinion propagation, Cellular automata, Personal authority.

Abstract. In this paper, the factor individual authority of communication subject was added to the

network opinion propagation model based on Cellular Automata, the trend of local public opinion in the process of propagation was considered, and the simulation experiment was carried out. The experimental results confirm the decisive role of the subject with power value in the process of public opinion dissemination. What more important is that the significant influence on the process of public opinion communication of subjects with high stubborn strength , high authority and holding a clear attitude towards public opinion is found. This kind of communication subject will form a small group of attitude isolation in the later period of public opinion dissemination. Finally, a case study of "Humiliating Mother Case" in Shandong was carried out. The above conclusions are confirmed by a handful of consistently opposed subjects in the case which proves that this model is effective.

Introduction

The spread of public opinion on the network mainly through QQ, micro-blog and other social software. The public opinion spreading is actually a process of complex social system evolution. Because of its homogeneity and discreteness, cellular automata have unique advantages in the study of the evolution of network public opinion. As early as 2002, Liu Mu-ren, a scholar, applied the cellular automata model to the study of public opinion communication [1]. Later, scholar Fang Wei used cellular automata to study the propagation of network public opinion, proposed the majority rule and cellular moving traversal algorithm [2], and then put forward the cooperative cellular automata model of public opinion propagation [3]. Recently scholars Mao Qian-ren and Wang Zhao-bin have used the cellular automata model to explore the control mechanism of network public opinion [4].

In the process of network public opinion dissemination, we find that the views of some mainstream media and someone with high attention greatly affects the direction of public opinion. This paper analysis the influence of the authority of individuals in the process of information dissemination, establish a reliable model of public opinion communication and have achieved the corresponding experimental simulation.

Construction of Cellular Automata Model for Public Opinion Propagation

Cells and Its State

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, -1 ( ) 0.3,

, -0.3 ( ) 0.3,

, -0.3 ( ) 1.

ij ij ij

suport S t

the state of cell neutrality S t

oppose S t

 ≤ ≤ −

= < < 

≤ ≤

(1)

In the process of public opinion communication, there are three types of people who are uninformed, disseminators and immune. The uninformed in the model is the cells whose state is 0.and immune refers to someone receive information but not spread it, because this kind of people will not to influence the process of public opinion dissemination, so here the model does not represent immune.

Cellular Neighborhood. In the cellular automata model, the evolution of the cellular state

depends on the state of the neighboring cells that around the central cell, and it must be clearly defined that each cell will be affected by which cells around it. Neighborhood models commonly used are Von Neumann (four neighborhood) and Moore (eight neighborhood).Here the model uses four neighborhood, the evolution of the state of each cell will be affected by of the adjacent four cellular state.

Considering the special situation of boundary cellular is needed when make the formulation of rules of evolution, here we take the periodic boundary conditions on the structure of cellular space, that is in a two-dimensional grid, setting its up and down sides, left and right sides connected with each other. In this way, we can appropriately describe the Infinite space environment of network public opinion.

Transformation Rules of Cellular States. In the process of public opinion spreading on the

internet, the discourse of the authority of different communication subjects will vary greatly. A large number of subjects’ attitude is in fact blindly, they tend to support representative characters or media that they follow. Therefore, in the model, an authoritative definitionR,R=( )rij n n× ,rij∈[0,1]is

defined for the cell, which is the authoritative vlue matrix of the cell subject. The personal authority is different from stubborn strength H which represents influence of the personality characteristics of subjects to spread or accept information. In the previous studies, the basic evolution rules of cell defined by scholars are as follows:

, 1 , 1 1, 1,

( 1) ( ) (1 ) ( ( ) ( ) ( ) ( )).

ij ij i j i j i j i j

S t+ =H×S t + −H ×Q S + t +St +S+ t +St (2)

In this formula, Qis neighborhood influence coefficient. It is assumed that the neighborhood of the four neighbors is equal, soQ=1 / 4. In this paper, we need to study the influence of the each cell subject with different authority values, therefore the influence of each neighbor cell on the central cell is related to its own authority.

In the process of public opinion information communication between cellular center and four neighbors cellular, it can be taken into account that if the emotional tendency of five personal values are positive, as S t Sij( ), i+1j( ),t Si1j( ),t Si j,+1( ),t Sij1( )t are all positive, then the five personal information

exchange will certainly make the results:

1 1 1 1

1 1 1 1

( 1) ( 1) ( 1) ( 1) ( 1)

( ) ( ) ( ) ( ) ( )

ij i j i j i j i j

ij i j i j i j i j

S t S t S t S t S t

S t S t S t S t S t

+ − + −

+ − + −

+ + + + + + + + + >

+ + + +

, , , ,

, , , ,

Similarly, if the values S t Sij( ), i+1,j( ),t Si−1,j( ),t Sij+1( ),t Sij−1( )t are all negative, then the results of

information exchange between the five people will make it possible that.

1 1 1 1

1 1 1 1

( 1) ( 1) ( 1) ( 1) ( 1)

( ) ( ) ( ) ( ) ( )

ij i j i j i j i j

ij i j i j i j i j

S t S t S t S t S t

S t S t S t S t S t

+ − + −

+ − + −

+ + + + + + + + + <

+ + + +

, , , ,

, , , ,

Therefore, when the public opinion information is transmitted between the central cell and the neighbors, the bias of the general public sentiment tendency is defined as

1, 1, , 1 , 1

1, 1, , 1 , 1

1, 1, , 1 , 1

( ) ( ) ( ) ( ) ( )

( ) , ( ), ( ), ( ), ( ), ( ) 0.

( ) ( ) ( ) ( ) ( )

ij i j i j i j i j

ij ij i j i j i j i j

ij i j i j i j i j

S t S t S t S t S t

D t S t S t S t S t S t

S t S t S t S t S t

(3)

And it will determine the tendency of public opinion of the five cellular units at the next moment. After center cell with state Sij( )t respectively communicate with cells( ,i j+1),( ,i j−1),(i+1, )j , (i−1, )j , the variations areKi j,+1( )t ,Ki j,−1( )t ,Ki+1,j( )t ,Ki−1,j( )t ,and

, 1 , 1

, 1 , 1

1, 1,

1, 1,

( ) ( , 1)[S ( ) ( )] / [ ( , 1) ( , )],

( ) ( , 1)[S ( ) ( )] / [ ( , 1) ( , )],

( ) ( 1, )[S ( ) ( )] / [ ( 1, ) ( , )],

( ) ( 1, )[S ( ) ( )

i j i j ij

i j i j ij

i j i j ij

i j i j ij

K t R i j t S t R i j R i j

K t R i j t S t R i j R i j

K t R i j t S t R i j R i j

K t R i j t S t

+ +

− −

+ +

− −

= + − + +

= − − − +

= + − + +

= − − ] / [ (R i−1, )j +R i j( , )].

(4)

According to the above discussion, the cellular state in the next time is affected by the current state of the neighbor cellular, authority value and stubborn strength of each subjects, and the bias of the general public sentiment tendency of the central cell and four neighborhood cellular. Therefore, cellular evolution rules is defined for:

, 1 , 1 1, 1,

( 1) [ ( ) ( ( ) ( ) ( ) ( )) ( , )] q D ( ).

ij ij i j i j i j i j ij

[image:3.612.200.415.292.450.2]

S t+ = S t + K + t +K t +K+ t +K t ×H i j + × t (5) Thereinq=0.001is parameters that affect local trends, andH is stubborn strength matrix.

Figure 1. Evolution process of cell state.

Simulation Results and Analysis

Model simulation is performed using MATLAB, and the specific steps are as follows:

(1)A two-dimensional cell space is created, that is 100 100× zero matrix, and we assign the random state to the initial state.

(2)A personal authority value matrixR=( )rij 100 100× ,rij∈[0,1], and the stubborn strength matrix

100 100

( , )

H =h i j × ,hij∈[0, 0.5] are created.

(3) The cellular state evolution rule is set up and 100 steps iterative operation is performed. The results of the cellular state in the simulation are shown in Fig. 1.

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[image:4.612.207.404.74.234.2]

Figure 2. Changes in the proportion of various subject attitudes.

In the results after the end of evolution, it is found that cells whose state approaching to cellular -1 or 1 tend to have smaller stubborn strength and more authoritative value. This kind of cells are easily affected by the cell in the neighborhood and has great influence on other cells in the neighborhood. The result of the evolution will eventually form a group with similar opinion tendency centered on this kind of cells. In addition, there are some cellular with distinct attitude but stubborn strength is high and authority value is smaller. Therefore, it is in an isolated state and out of tune with the state of public opinion formed by the surrounding cells. There are some cellular with high stubborn strength and authoritative value holds a clear attitude. In the final evolution, these types of cells generally form an isolated small population. Most of the cell belongs to a kind of stubborn low strength and authoritative value is too low, representing the masses who follow the tide in the process of public opinion spreading.

In the process of cellular evolution, according to the attitude of cells set previous, tracking the change of the proportion of three attitudes, opposition, neutrality and support, we get the results of Fig. 2. The results clearly show that in the cellular evolution, cells with neutral attitude gradually differentiate towards a clear attitude and direction, and the subjects who hold opposing and supporting attitudes continue to absorb neutrals, and the proportion continues to expand.

[image:4.612.200.413.559.714.2]

In order to study the influence of personal authority in the dissemination of public opinion, the value greater than 0.9 is changed to 0.2, and the value less than 0.2 is changed to 0.9 in the above simulation of cells authority value matrix. Then we again carries on the simulation experiment, the simulation results are obtained in Fig.3. Comparing the results of two experiments in cells evolution after 100 times, it can be found that the center of public opinion has changed. So it can be determined that the personal authority did have a great impact on the process of public opinion spreading.

Figure 3. Evolution results after changing personal authority values.

0 20 40 60 80 100 120

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

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[image:5.612.210.402.74.231.2]

Figure 4. The trend of public opinion of "Humiliating Mother Case".

Case Study

In order to further verify the model established in this paper and the accuracy of the parameters, the model is used to simulate the actual case. Shandong "Humiliating Mother Case" took place in April 14, 2016. In March 23, 2017, the Southern Weekend reported the incident, and it instantly became the focus of public opinion. A lot of people doubt the court's judgment, and some people think that murder should be sentenced. In March 26th, the event was clicked more than 500 million. At the beginning of the online voting, 168 thousands people supported the retrial while 16.4 thousand people objected.

The initial state of cells in the model is adjusted according to the proportion of 10:1 and keep the state of neutral cell. Then, the results of public opinion evolution in this case are obtained by experiment simulation as Fig.4. That can be seen in the early stage of evolution, the neutral people divided into two directions: opposition and support, and the proportion of opponents increased slightly then dropped to a lower level because of the low proportion of their supporters. This evolution is consistent with the 1.64:0.08 ratio of supporters and opponents in later news surveys.

By observing the evolution process of public opinion, we can find that in the cellular state graph after 100 steps of evolution Fig.5 (d) there are some isolated small groups mentioned above due to the existence of a stubborn higher strength, greater authority value cellular maintained a clear attitude. This also explains that there are still a small number of people hold an attitude of opposition though the public opinion in this case is developing in a one-sided situation. Thus, the model established in this paper conforms to the actual situation and the model parameters are more accurate.

[image:5.612.199.414.551.725.2]
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Conclusion

The personal authority of the subject of communication is added to the cellular automata model of public opinion propagation, and the process of public opinion propagation and the results are obtained. Then the authority value of the subject is adjusted, the results obtained of the evolution compared with the last time, it is found that the center of cell state is greatly shifted after evolution 100 steps. And the importance of subject authority of the communication is verified. Finally, through case study, the reason of that a small number of people insist on their own views in the “Humiliating Mother case” was found, that proves the important influence of some subjects with stubborn high strength, greater authority and clear attitude in the process of dissemination of public opinion.

Reference

[1] Liu Muren, Deng Minyi. Cellular automata model of public opinion communication [J]. Journal of Guangxi Normal University, 2002.

[2] Fang Wei, He Hao, Sun Kai. Research on network public opinion propagation model based on cellular automata [J]. Computer application, 2010.

[3] Fang Wei, He Hao, song Liang Liang. The cooperative cellular automata model of Internet public opinion propagation [J]. Computer application, 2012.

Figure

Figure 1. Evolution process of cell state.
Figure 2. Changes in the proportion of various subject attitudes.
Figure 5. Simulation evolution process of "Humiliating Mother Case".

References

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